B\"acklund transformations for high-order constrained flows of the AKNS hierarchy: canonicity and spectrality property
Abstract
New infinite number of one- and two-point B\"acklund transformations (BTs) with explicit expressions are constructed for the high-order constrained flows of the AKNS hierarchy. It is shown that these BTs are canonical transformations including B\"acklund parameter η and a spectrality property holds with respect to η and the 'conjugated' variable μ for which the point (η, μ) belongs to the spectral curve. Also the formulas of m-times repeated Darboux transformations for the high-order constrained flows of the AKNS hierarchy are presented.
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